MinT - Best Known (246−137, 246, s)-Nets in Base 4

Best Known (246−137, 246, s)-Nets in Base 4

(246−137, 246, 130)-Net over F₄ — Constructive and digital

Digital (109, 246, 130)-net over F₄, using

t-expansion [i] based on digital (105, 246, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(246−137, 246, 165)-Net over F₄ — Digital

Digital (109, 246, 165)-net over F₄, using

net from sequence [i] based on digital (109, 164)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
  - Drinfeld modules of rank 1 [i]

(246−137, 246, 1231)-Net in Base 4 — Upper bound on s

There is no (109, 246, 1232)-net in base 4, because

1 times m-reduction [i] would yield (109, 245, 1232)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3213 000372 973706 187241 793319 233045 842074 247092 587624 423260 776236 615782 319900 125681 485994 994532 646064 232616 184716 438732 755587 204687 488209 081975 951859 > 4²⁴⁵ [i]